I would work on recall, and desensitize him to what is making the dog bark.
My dog used to bark in our yard, I'd call him, he'd keep barking, and I'd have to go get him and bring him in.
I addressed this annoying routine by working on his recall. I practiced and practiced getting him to come to me, and gave him treats every time he did.
I also would randomly give a really good treat, like a nice bit of leftover meat. Now he's quite reliable. There was a raccoon in the yard a few nights ago, and he didn't come, but it's rare that he doesn't.
So now my dog will bark, but as soon as I hear it, I call him, and he comes in.
Oh, and another thing I did was to get him to be calm around the things that were provoking the barking. I think you've got it tough, having your backyard surrounded by barking dogs, but maybe you could reward them with treats whenever they *don't* bark at the dogs, and maybe they'll start to calm down and not see those dogs as a trigger.
I really get that it's a pain to have to supervise, but some time put in now could pay off later.